How is Trask alive in X-Men: The Last Stand given the plot of X-Men: Days of Future Past?

Question

At the start of X-Men: Days of Future Past, it was explained that Trask was assassinated by Mystique in 1973 and the whole movie was basically about Wolverine going back in time to prevent that assassination. The mutants at the beginning of the film seem to be in continuity with the ones from X-Men: The Last Stand, so I'm assuming this part of X-Men: Days of Future Past is in the same timeline as X-Men: The Last Stand.

But then Trask does appear at the beginning of X-Men: The Last Stand as Secretary Trask, therefore the assassination could not have taken place in the first place. Is this a big gaping plot hole or did I read the continuity wrongly?

**Note: I'm aware that Trask was played by different actors in both movies. My question is on the continuity of Trask as a character in the movies. Given that the whole plot of X-Men: Days of Future Past revolves around preventing Trask's assassination, it would be a plot hole significant enough to invalidate the entire movie if the assassination never took place in the first place.

Answer 1

There can be two answers:

First: Simply put, both are not the same person. In X-Men: The Last Stand, Bill Duke's character was never called Bolivar Trask but just Trask. In X-Men: Days of Future Past, Peter Dinklage's character was called Bolivar Trask.

Both have different ethnicities, ages, careers, heights, and behaviors. The only common thing was the surname. Also, even in the comics, Bolivar Trask was not the only Trask.

This explanation is speculated by many fans and used in fandom pages too, but has no official backing, and even the director's words contradict this theory as shared below.

Second: X-Men movies continuity-wise never make sense, characters change ethnicity, age, and whatnot anyways. Which is kind of true as per the director's words:

Speaking exclusively to SciFiNow for the massive behind the scenes in the new issue, Bryan Singer simply hopes you’ll forget about them and move on.

"Some things you let go," Singer admits. "In X-Men, 3 Bolivar Trask was an African-American guy, in X-Men 1 I personally wrote the line that of course I now regret: 'When I was 17, I met a young man named Erik Lensherr' and then in X-Men: First Class I changed that!" he laughs.

"Some of these I hope the audience will forget about but for the bulk of it I pay attention to the universe."

So in an X-men movie universe where Jubilee, Angel, and many others change age by decades, Trask can change ethnicity, and Wolverine's claws magically switch between bone and adamantium, the character being magically alive is not surprising. Maybe he survived by the same magic that changed his ethnicity, height, and personality.